The average velocity during a time interval cannot tell us how fast or in what direction a particle is moving at any given time during the interval. To calculate this, it is important to know the instantaneous velocity, which is the velocity at a specific instant of time or at a specific point along the path. Instantaneous velocity is the quantity that measures how fast an object is moving along its path. In other words, the instantaneous velocity vx of an object is the limit of the average velocity as the elapsed time approaches zero, or the derivative of x with respect to t.
Like average velocity, the instantaneous velocity is a vector with the dimensions of length per unit of time. Instantaneous velocity can have both positive and negative values. A positive value of instantaneous velocity implies increasing x, and the motion is in the positive x-direction. A negative value of instantaneous velocity implies decreasing x, and the motion is in the negative x-direction.
Instantaneous speed is the magnitude of the instantaneous velocity. For example, a particle with instantaneous velocity −10 m/s and a particle with instantaneous velocity +10 m/s have the same instantaneous speed, but are traveling in opposite directions.
This text is adapted from Openstax, University Physics Volume 1, Section 3.2: Instantaneous Velocity and Speed.
